Question

xy=15
2x+3y=21
sistema do segundo grau

Answer 1

xy = 15
2x + 3y = 21

x = 15
       y

2x + 3y = 21

2.15 + 3y = 21
    y

mmc = y

30 + 3y² = 21y
    y             y

30 + 3y² = 21y
3y² - 21y + 30 = 0 (:3)
y² - 7y + 10 = 0

a = 1; b = - 7; c = 10

Δ = b² - 4ac
Δ = (-7)² - 4.1.10
Δ = 49 - 40
Δ = 9

y = - b +/- √Δ = - ( - 7) +/- √9
           2a                  2.1

y = 7 + 3 = 10 = 5
        2         2

y = 7 - 3 = 4  =  2
        2       2
=================
y = 5
x = 15  =  15  =  3
       y        5
x = 3
=================
y = 2
x =  15 = 15  
        y      2

x = 15/2
=======================
y = 5
2x + 3y = 21
2x + 3.5 = 21
2x + 15 = 21
2x = 21 - 15
2x = 6
x = 6/2
x = 3
======================
y = 2
2x + 3y = 21
2x + 3.2 = 21
2x + 6 = 21
2x = 21 - 6
2x = 15
x = 15/2

R.: y = 5 / x = 3 ou y = 2 e x = 15/2